Pressure Volume Mass Equation Explained

This calculator works out the pressure, volume, or mass of an ideal gas when you know the other two and the temperature. You enter any two of the three quantities plus the temperature, and it returns the missing value using the ideal gas law. The result is given in the unit you choose for the unknown quantity.

Formula

The equation that links pressure, volume, and mass (through the number of moles) is the ideal gas law:

PV = nRT

Where:

• P = pressure of the gas (in pascals, Pa, or kilopascals, kPa)
• V = volume of the gas (in cubic meters, m³, or liters, L)
• n = amount of gas in moles (mol)
• R = universal gas constant (8.314 J/(mol·K) when using Pa·m³, or 8.314 kPa·L/(mol·K) when using kPa and L)
• T = absolute temperature (in kelvin, K)

To find mass, you multiply the number of moles by the molar mass of the gas (in g/mol): mass = n × molar mass. So the full relationship becomes PV = (mass / molar mass) × RT. This is the standard form used in chemistry and physics when you need to solve for any one of the four variables.

Worked Example

Using the default values from the calculator above: pressure = 101.325 kPa, volume = 22.414 L, temperature = 273.15 K, and amount = 1 mol. We want to find the missing quantity, which in this case is the amount of gas (n).

1. Start with the ideal gas law: PV = nRT
2. Rearrange to solve for n: n = PV / (RT)
3. Substitute the values: n = (101.325 × 22.414) / (8.314 × 273.15)
4. Calculate the numerator: 101.325 × 22.414 = 2271.1
5. Calculate the denominator: 8.314 × 273.15 = 2271.1
6. Divide: 2271.1 / 2271.1 = 1.000

The result is 1.000 mol, which matches the default amount. This shows that at standard temperature and pressure (STP), one mole of an ideal gas occupies 22.414 liters.

When to Use This Equation

The ideal gas law applies to gases that behave ideally—meaning the gas particles have negligible volume and no intermolecular forces. This is a good approximation for most real gases at low pressure and high temperature. You would use it in:

• Chemistry labs to find the molar mass of an unknown gas
• Engineering to size gas cylinders or design pneumatic systems
• Physics problems involving gas behavior in closed containers
• Environmental science to estimate gas emissions from a known volume

For real gases at high pressure or low temperature, the ideal gas law becomes less accurate, and you would need the van der Waals equation or other real-gas models.

How to Read the Result

The calculator returns the missing quantity in the unit you selected. If you entered pressure in kPa, volume in L, and temperature in K, the result for n will be in moles. To convert moles to mass, multiply by the molar mass of the specific gas. For example, if you have 2 moles of oxygen (O₂, molar mass 32 g/mol), the mass is 64 grams. Always check that your units are consistent—mixing kPa with m³ will give a different value for R, so use the same unit system throughout.

Common Mistakes and Misconceptions

One common mistake is forgetting to convert temperature to kelvin. The ideal gas law requires absolute temperature, so Celsius or Fahrenheit values must be converted by adding 273.15 (for Celsius) or using the appropriate formula. Another error is mixing units: if you use pressure in atm, you must use R = 0.0821 L·atm/(mol·K), not 8.314. Also, remember that the equation gives moles, not mass directly—many people forget to multiply by molar mass when they need grams.

A frequent misconception is that the ideal gas law works for all gases under all conditions. It does not—real gases deviate significantly at high pressures (where molecules are close together) and low temperatures (where intermolecular forces become significant). For such cases, use the van der Waals equation or compressibility factors.

Alternatives and Extensions

When the ideal gas law is not accurate enough, you can use:

• Van der Waals equation: (P + a(n/V)²)(V – nb) = nRT, where a and b are gas-specific constants.
• Compressibility factor (Z): PV = ZnRT, where Z is a correction factor from experimental data.
• Combined gas law: Pâ‚�Vâ‚�/Tâ‚� = Pâ‚‚Vâ‚‚/Tâ‚‚, for comparing two states of the same gas without needing moles.

For mixtures, you use the partial pressures (Dalton’s law) and sum the moles of each component. The ideal gas law also forms the basis for calculating density: density = (P × molar mass) / (RT).

Frequently Asked Questions

How do I find mass from pressure and volume?

First, solve the ideal gas law for n (moles): n = PV / (RT). Then multiply by the molar mass of the gas. For example, if you have a 10 L container at 200 kPa and 300 K with nitrogen (N₂, molar mass 28 g/mol), n = (200 × 10) / (8.314 × 300) = 0.802 mol, so mass = 0.802 × 28 = 22.5 g.

What is the value of R in different units?

The gas constant R depends on the units of pressure and volume. Common values: 8.314 J/(mol·K) (SI), 0.0821 L·atm/(mol·K), 62.36 L·mmHg/(mol·K), and 8.314 kPa·L/(mol·K). Always match R to your pressure and volume units.

Does the ideal gas law work for liquids?

No, the ideal gas law only applies to gases. Liquids are nearly incompressible and have strong intermolecular forces, so their pressure-volume relationship is completely different. For liquids, you would use other equations of state or empirical data.

What is STP and why is it important?

STP (Standard Temperature and Pressure) is defined as 0°C (273.15 K) and 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies 22.414 liters. This is a convenient reference point for comparing gas volumes and calculating molar masses.

Can I use this equation for a gas mixture?

Yes, but you must treat the mixture as a whole. The total moles (n) is the sum of the moles of each component, and the pressure is the total pressure. For partial pressures, you can use Dalton’s law: each gas contributes a partial pressure proportional to its mole fraction.

Why do I need to convert temperature to kelvin?

The kelvin scale starts at absolute zero, where gas molecules have minimal kinetic energy. The ideal gas law is based on the relationship between temperature and molecular motion, which is linear only when using an absolute scale. Celsius or Fahrenheit would give negative or zero values that break the equation.

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in p | Pressure | kPa | 101.325 | 0
in v | Volume | L | 22.414 | 0
in n | Amount of gas | mol | 1 | 0
in t | Temperature | K | 273.15 | 0
out result | Missing quantity | - | (p * v) / (8.314 * t) | 3